Question

A gas is filled in a vessel of volume V at 35 degree centigrade.To what temperature should it be heated in order that half of the gas may escape out?

Answer 1

The new temperature should be 343 °C.

Explanation:

Given

The volume `V_1` of a gas at a temperature `T_1`.
A second volume `V_2`

Find

The second temperature `T_2`

Strategy

A problem involving two gas volumes and two temperatures must be a Charles' Law problem.

The formula for Charles' Law is

`color(blue)(bar(ul(|color(white)(a/a)V_1/T_1 = V_2/T_2color(white)(a/a)|)))" "`

Rearrange Charles' Law to get

`T_2 = T_1 × V_2/V_1`

Solution

In your problem, we must calculate the temperature at which the new volume will be twice the original volume. We have

`V_1 = V; color(white)(l)T_1 = "35 + 273.15 K = 308.15 K"`
`V_2 = 2V; T_2 = "?"`

∴ `T_2 = "308.15 K" × (2 cancel(V))/(cancelV) = "616.30 K = 343 °C"`

The new temperature is 343 °C.